Question

On Monday a park event has 150 visitors. On Tuesday it has 260 visitors. Using this rate of increase estimate the count of visitors for Wednesday?

Answer 1

Monday to Tuesday's increase is `73 1/3%` `larrul("Not an estimate")`
Count for Wednesday is `450 2/3` `larrul("Not an estimate")`

`color(brown)("See the other answer for an estimated solution")`

Explanation:

`color(blue)("Part 1")`

change for Monday to Tuesday is expressed as a fraction of the original count and is:

`(260-150)/150 = 110/150`

To change this into a percentage the bottom number (denominator) need to become 100.

Multiply by 1 and you do not change the value. However, 1 comes in many forms.

`color(green)((110)/(150)color(red)(xx1))`

`color(green)((110)/(150)color(red)(xx(color(white)("d")2/3color(white)("d"))/(2/3)))color(white)("d")=color(white)("d")(73 1/3)/100 rarr 73 1/3%`

The above is an exact value not as an estimate as stated in the question.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Part 2")`

Tuesday's count is given as 260

So the same increase proportion for Tuesday to Wednesday is

`73 1/3%` of 260

`(73 1/3)/100xx260`

But this is the same as

`73 1/3xx1/100 xx 260`

`73 1/3xx(26cancel(0))/(10cancel(0))`

`(cancel(220)^22)/3xx26/cancel(10)^1 = 190 2/3`

So the total coming through the door on Wednesday is

`260+190 2/3 = 450 2/3`

Call it 451

Answer 2

`color(brown)("The estimated solution")`
The problem about 'ESTIMATES' is that unless defined you do not know the degree of precision required.

`color(brown)("Only answered the first part")`

Explanation:

`color(blue)("ESTIMATING the percentage change Monday to Tuesday")`

`260 - 150 = 110` round this to 100 giving

`100/150`

Known that `2/3xx150=100`

`(2/3xx100)/(2/3xx150)`

`(2/3xx100)xx1/100 ->(2/3xx100)%`

estimate `1/3` of `100` as 30 so `2/3` would be 60 giving

So the ESTIMATED percentage change is `60%`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(brown)("Lets see what the error is on this")`

The exact solution is `73 1/3%`

So the degree of error is

`(73 1/3-60)/60 -> 22.222...%" error"`